I'm going to be offering a new accessory for my "Shrew Hawk" that's on my web site
www.shrewbows.com It's a way to carry your hawk when you don't want it strapped to your belt. This is not a new idea. In Allan Eccarts book "The Frontiersman", he wrote of Simon Greathouse, a trapper/trader who carried a tomahawk in a leather sheath tucked under his arm. There's also a picture of a hawk with a sheath in a Museum that was on the Lewis & Clark Expedition that was carried in a sheath on a strap over the shoulder.
I contracted Art Vincent of Cedar Ridge Leather Works to make a similar setup for the Shrew Hawk. Art also makes the Shrew Mantis Quiver for me. He made the main body of the sheath out of tooling leather and molded it to the shape of the hawk and stained it and the strap in brown. The strap is fitted with a brass buckle to make it fully adjustable. Here's the results of Arts fine craftsmanship.
I like to carry my hawk high so as to keep it controlled under my arm. That way it won't swing around when I'm bending or moving around.